Answer:AB = 13 and BC = 9.
Explanation:
We can use the fact that in a triangle ABC, the length of one side is less than the sum of the other two sides, and greater than the difference of the other two sides.
So, we have:
AC < AB + BC ...(1)
AC > AB - BC ...(2)
BC < AB + AC ...(3)
BC > AC - AB ...(4)
We are given that AC = 22 and BC = 2x + 1 and AB = 4x - 3.
Substituting these values in equation (1), we get:
22 < (4x - 3) + (2x + 1)
Simplifying the above inequality, we get:
22 < 6x - 2
24 < 6x
x > 4
Substituting the value of x in BC, we get:
BC = 2x + 1 = 2(4) + 1 = 9
Substituting the value of x in AB, we get:
AB = 4x - 3 = 4(4) - 3 = 13
Therefore, AB = 13 and BC = 9.